Non-Markovian out-of-equilibrium dynamics: A general numerical procedure to construct time-dependent memory kernels for coarse-grained observables

We present a numerical method to compute non-equilibrium memory kernels based on experimental data or molecular dynamics simulations. The procedure uses a recasting of the non-stationary generalized Langevin equation, in which we expand the memory kernel in a series that can be reconstructed iteratively. Each term in the series can be computed based solely on knowledge of the two-time auto-correlation function of the observable of interest. As a proof of principle, we apply the method to crystallization from a super-cooled Lennard Jones melt. We analyze the nucleation and growth dynamics of crystallites and observe that the memory kernel has a time extent that is about one order of magnitude larger than the typical timescale needed for a particle to be attached to the crystallite in the growth regime

Systematic derivation of Generalized Langevin Equations for coarse-graining and bridge-scaling procedures

In many branches of physics, one must often deal with processes involving a huge number of degrees of freedom. Instead of describing the dynamics of each individual of them, one rather wants to characterize the process of interest via a small set of observ- ables that capture its main features of the process. Even if the microscopic dynamics can be resolved using Newton’s equations of motion, it quickly becomes a computation- ally very expensive calculation to make. It is however much more convenient to come up with a self-consistent equation of motion for the ’global’ observable of interest itself in order to reduce the complexity of the problem. The development of the Mori-Zwanzig formalism in the 1960’s allowed to systematically derive such equations for arbitrary observables in stationary processes. This framework, derived from first principles by means of projection operator techniques, proves the structure of what is now known as the Generalized Langevin Equation, i.e. a stochastic equation of motion which a priori exhibits memory effects in the form on non-localities in time. We propose to extend the formalism and its corollaries to a broad class of out-of- equilibrium processes. We show that the structure of the Generalized Langevin Equa- tion is overall robust but must be adapted to account for the non-stationary dynamics [1,2]. The function that controls memory effects the stochastic term are related through a relation that can be associated to fluctuation-dissipation theorems. This formalism is very convenient to study two-time auto-correlation functions for which we can write a self-consistent differential equation as well. We finally show a new method to evaluate the memory function from numerical or experimental data [3]

Reconsidering the structure of nucleation theories

We discuss the structure of the equation of motion that governs nucleation processes at first order phase transitions. From the underlying microscopic dynamics of a nucleating system, we derive by means of a non-equilibrium projection operator formalism the equation of motion for the size distribution of the nuclei. The equation is exact, i.e. the derivation does not contain approximations. To assess the impact of memory, we express the equation of motion in a form that allows for direct comparison to the Markovian limit. As a numerical test, we have simulated crystal nucleation from a supersaturated melt of particles interacting via a Lennard-Jones potential. The simulation data show effects of non-Markovian dynamics

Memory effects in the Fermi-Pasta-Ulam Model

We study the Intermediate Scattering Function (ISF) of the strongly-nonlinear Fermi-Pasta Ulam Model at thermal equilibrium, using both numerical and analytical methods. From the molecular dynamics simulations we distinguish two limit regimes, as the system behaves as an ideal gas at high temperature and as a harmonic chain for low excitations. At intermediate temperatures the ISF relaxes to equilibrium in a nontrivial fashion. We then calculate analytically the Taylor coefficients of the ISF to arbitrarily high orders (the specific, simple shape of the two-body interaction allows us to derive an iterative scheme for these.) The results of the recursion are in good agreement with the numerical ones. Via an estimate of the complete series expansion of the scattering function, we can reconstruct within a certain temperature range its coarse-grained dynamics. This is governed by a memory-dependent Generalized Langevin Equation (GLE), which can be derived via projection operator techniques. Moreover, by analyzing the first series coefficients of the ISF, we can extract a parameter associated to the strength of the memory effects in the dynamics

Percolation in suspensions of polydisperse hard rods : quasi-universality and finite-size effects

We present a study of connectivity percolation in suspensions of hard spherocylinders by means of Monte Carlo simulation and connectedness percolation theory. We focus attention on polydispersity in the length, the diameter and the connectedness criterion, and invoke bimodal, Gaussian and Weibull distributions for these. The main finding from our simulations is that the percolation threshold shows quasi universal behaviour, i.e., to a good approximation it depends only on certain cumulants of the full size and connectivity distribution. Our connectedness percolation theory hinges on a Lee-Parsons type of closure recently put forward that improves upon the often-used second virial approximation [ArXiv e-prints, May 2015, 1505.07660]. The theory predicts exact universality. Theory and simulation agree quantitatively for aspect ratios in excess of 20, if we include the connectivity range in our definition of the aspect ratio of the particles. We further discuss the mechanism of cluster growth that, remarkably, differs between systems that are polydisperse in length and in width, and exhibits non-universal aspects.Comment: 7 figure

Eastern Beringia and beyond: Late Wisconsinan and Holocene landscape dynamics along the Yukon Coastal Plain, Canada

Terrestrial permafrost archives along the Yukon Coastal Plain (northwest Canada) have recorded landscape development and environmental change since the Late Wisconsinan at the interface of unglaciated Beringia (i.e. Komakuk Beach) and the northwestern limit of the Laurentide Ice Sheet (i.e. Herschel Island). The objective of this paper is to compare the late glacial and Holocene landscape development on both sides of the former ice margin based on permafrost sequences and ground ice. Analyses at these sites involved a multi-proxy approach including: sedimentology, cryostratigraphy, palaeoecology of ostracods, stable water isotopes in ground ice, hydrochemistry, and AMS radiocarbon and infrared stimulated luminescence (IRSL) dating. AMS and IRSL age determinations yielded full glacial ages at Komakuk Beach that is the northeastern limit of ice-free Beringia. Herschel Island to the east marks the Late Wisconsinan limit of the northwest Laurentide Ice Sheet and is composed of ice-thrust sediments containing plant detritus as young as 16.2 cal ka BP that might provide a maximum age on ice arrival. Late Wisconsinan ice wedges with sediment-rich fillings on Herschel Island are depleted in heavy oxygen isotopes (mean δ18O of −29.1‰); this, together with low dexcess values, indicates colder-than-modern winter temperatures and probably reduced snow depths. Grain-size distribution and fossil ostracod assemblages indicate that deglaciation of the Herschel Island icethrust moraine was accompanied by alluvial, proluvial, and eolian sedimentation on the adjacent unglaciated Yukon Coastal Plain until ~11 cal ka BP during a period of low glacio-eustatic sea level. The late glacial–Holocene transition was marked by higher-than-modern summer temperatures leading to permafrost degradation that began no later than 11.2 cal ka BP and caused a regional thaw unconformity. Cryostructures and ice wedges were truncated while organic matter was incorporated and soluble ions were leached in the thaw zone. Thermokarst activity led to the formation of ice-wedge casts and deposition of thermokarst lake sediments. These were subsequently covered by rapidly accumulating peat during the early Holocene Thermal Maximum. A rising permafrost table, reduced peat accumulation, and extensive ice-wedge growth resulted from climate cooling starting in the middle Holocene until the late 20th century. The reconstruction of palaeolandscape dynamics on the Yukon Coastal Plain and the eastern Beringian edge contributes to unraveling the linkages between ice sheet, ocean, and permafrost that have existed since the Late Wisconsinan

On the "generalized Generalized Langevin Equation"

In molecular dynamics simulations and single molecule experiments, observables are usually measured along dynamic trajectories and then averaged over an ensemble ("bundle") of trajectories. Under stationary conditions, the time-evolution of such averages is described by the generalized Langevin equation. In contrast, if the dynamics is not stationary, it is not a priori clear which form the equation of motion for an averaged observable has. We employ the formalism of time-dependent projection operator techniques to derive the equation of motion for a non-equilibrium trajectory-averaged observable as well as for its non-stationary auto-correlation function. The equation is similar in structure to the generalized Langevin equation, but exhibits a time-dependent memory kernel as well as a fluctuating force that implicitly depends on the initial conditions of the process. We also derive a relation between this memory kernel and the autocorrelation function of the fluctuating force that has a structure similar to a fluctuation-dissipation relation. In addition, we show how the choice of the projection operator allows to relate the Taylor expansion of the memory kernel to data that is accessible in MD simulations and experiments, thus allowing to construct the equation of motion. As a numerical example, the procedure is applied to Brownian motion initialized in non-equilibrium conditions, and is shown to be consistent with direct measurements from simulations

Photonic quantum state transfer between a cold atomic gas and a crystal

Interfacing fundamentally different quantum systems is key to build future hybrid quantum networks. Such heterogeneous networks offer superior capabilities compared to their homogeneous counterparts as they merge individual advantages of disparate quantum nodes in a single network architecture. However, only very few investigations on optical hybrid-interconnections have been carried out due to the high fundamental and technological challenges, which involve e.g. wavelength and bandwidth matching of the interfacing photons. Here we report the first optical quantum interconnection between two disparate matter quantum systems with photon storage capabilities. We show that a quantum state can be faithfully transferred between a cold atomic ensemble and a rare-earth doped crystal via a single photon at telecommunication wavelength, using cascaded quantum frequency conversion. We first demonstrate that quantum correlations between a photon and a single collective spin excitation in the cold atomic ensemble can be transferred onto the solid-state system. We also show that single-photon time-bin qubits generated in the cold atomic ensemble can be converted, stored and retrieved from the crystal with a conditional qubit fidelity of more than $85\%$. Our results open prospects to optically connect quantum nodes with different capabilities and represent an important step towards the realization of large-scale hybrid quantum networks